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The mathematical theory of juggling
Zamboj, Michal ; Slavík, Antonín (advisor) ; Halas, Zdeněk (referee)
Title: The mathematical theory of juggling Author: Bc. Michal Zamboj Department: Department of Mathematics Education Supervisor: RNDr. Antonín Slavík, Ph.D. Abstract: This diploma thesis extends the bachelor thesis of the same name. It deals with the graphic representation of juggling sequences by the cyclic diagram. Using the Burnside theorem and cyclic diagrams, we calculate the number of all genera- tors of juggling sequences. The relation between juggling and the theory of braids is described as well. The mathematical model of inside and outside throws is made from an empirical observation of trajectories of balls. Braids of juggling sequences and their attributes are provided using a real model of ladder. A sketch of the proof of the theorem that any braid is juggleable is given as well.
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Combinatorial sequences and divisibility
Michalik, Jindřich ; Slavík, Antonín (advisor)
This work contains an overview of the results concerning number-theoretic pro- perties of some significant combinatorial sequences such as factorials, binomial coef- ficients, Fibonacci and Catalan numbers. These properties include parity, primality, prime power divisibility, coprimality etc. A substantial part of the text should be accessible to gifted high school students, the results are illustrated with examples. 1
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Reeducating university students' mechanical knowledge in mathematical analysis
Šmídová, Kristýna ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
The topic of this thesis is the didactics of mathematical analysis. The thesis describes selected observations from the reeducation in an individual tutoring environment of for- mal knowledge of university students in the field of calculus. The aim of the thesis is to describe what formal knowledge appeared, to describe and evaluate selected reeducation interventions and on this basis formulate appropriate methodological recommendation. In the first chapter we deal with the contradiction between definition and concept concept of students, we outline how to convey to students the purpose of definitions and we suggest how to teach students to work with definitions properly, including understanding quan- tified propositions. In the second chapter we present the theory of process and concept together with the generic model theory. In the third chapter we explain the methods of work with students and the methods of the analysis of videos from tutoring. In the fourth chapter we analyze cognitive processes of the concept of sequence limits. KEYWORDS reeducation, individual tutoring, mechanical knowledge, calculus, definitions, quantified proposition, infinity, sequence, limit 1
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Teaching geometric series through CLIL method with using of German language
Korcová, Aneta ; Moravcová, Vlasta (advisor) ; Hromadová, Jana (referee)
The core of the thesis is the realization of three lessons of mathematics conducted in accordance with the CLIL method, which integrates the teaching a non-linguistic subject with foreign language teaching. The topic of the lessons was non-finite geometric series and the chosen foreign language was German. The first part of the thesis introduces key definitions and theorems concerning sequences and geometric series. Comparisons are drawn between approaches of the Czech Republic and two German-speaking countries, Austria and Germany, in relationship to the teaching non-finite geometric series. Furthermore, available teaching materials of the selected countries are compared and applied visualized problems which appear in them are analysed. In the second part, the CLIL teaching method is presented together with the methodology according to which the lessons were prepared, realized and subsequently assessed. To conclude, the thesis presents a detailed analysis of the preparation and progress of the lessons, including the reflection. The appendix comprises of the utilized teaching materials as well as a range of the solved problems.
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Combinatorial sequences and divisibility
Michalik, Jindřich ; Slavík, Antonín (advisor)
This work contains an overview of the results concerning number-theoretic pro- perties of some significant combinatorial sequences such as factorials, binomial coef- ficients, Fibonacci and Catalan numbers. These properties include parity, primality, prime power divisibility, coprimality etc. A substantial part of the text should be accessible to gifted high school students, the results are illustrated with examples. 1
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Combinatorial sequences and divisibility
Michalik, Jindřich ; Slavík, Antonín (advisor) ; Staněk, Jakub (referee)
This work contains an overview of the results concerning number-theoretic pro- perties of some significant combinatorial sequences such as factorials, binomial coef- ficients, Fibonacci and Catalan numbers. These properties include parity, primality, prime power divisibility, coprimality etc. A substantial part of the text should be accessible to gifted high school students, the results are illustrated with examples. 1
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The mathematical theory of juggling
Zamboj, Michal ; Slavík, Antonín (advisor) ; Halas, Zdeněk (referee)
Title: The mathematical theory of juggling Author: Bc. Michal Zamboj Department: Department of Mathematics Education Supervisor: RNDr. Antonín Slavík, Ph.D. Abstract: This diploma thesis extends the bachelor thesis of the same name. It deals with the graphic representation of juggling sequences by the cyclic diagram. Using the Burnside theorem and cyclic diagrams, we calculate the number of all genera- tors of juggling sequences. The relation between juggling and the theory of braids is described as well. The mathematical model of inside and outside throws is made from an empirical observation of trajectories of balls. Braids of juggling sequences and their attributes are provided using a real model of ladder. A sketch of the proof of the theorem that any braid is juggleable is given as well.
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Image Processing Chain
Ptáček, Tomáš ; Zuzaňák, Jiří (referee) ; Juránek, Roman (advisor)
This master's thesis deals with implementation of a system for creating general image operations using an image processing chain. The text introduces the concept of image processing using chains and shows its advantages and possibilities. Furthermore, the text focuses on the detailed design of a system based on that concept. The system was successfully implemented and tested, while the results were described and discussed. Finally, the system is shown in a practical application of several image processing tasks.
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Sequences and series (not only) in word problems
FIŘTOVÁ, Petra
The dissertation is comprised of list of tasks with the sequences and set of numbers used to the high schools. This issue is very extensive and the dissertation is focused on application of the sequesces and set of numberss in word mathematic tasks which are thematicly devided into particular tasks according to their specialization. The tasks are classi?ed from the point of historical view as well as from the point of application view - in planimetry and stereometry, in ?nancial mathematics etc. In the part dedicated to sequences is stated extra chapter focused on excersises from mathematic olympics for high schools.
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